This is only marginally useful. It is not, for example, an effective way to maintain a login session, which will obviously break down on opening another window, or browser restarts, etc. Plus the fact that any website could then steal any user session.
Since this is by far the most useful reason to have session cookies (there are other valid uses, but plenty more abuses), this seems mostly like just a clever hack to me.
Yeah, this seems like a good thing to be able to turn off - I don't want the websites I visit to share information between each other.
Be sure to read the "Security considerations" paragraph carefully before using this.